Theory of complex-coordinate transformation acoustics for non-Hermitian metamaterials

Transformation acoustics (TA) has emerged as a powerful tool for designing several intriguing conceptual devices, which can manipulate acoustic waves in a flexible manner, yet their applications are limited in Hermitian materials. In this work, we propose the theory of complex-coordinate transformation acoustics (CCTA) and verify the effectiveness in realizing acoustic non-Hermitian metamaterials. Especially, we apply this theory for the first time to the design of acoustic parity-time ( PT ) and antisymmetric parity-time ( APT ) metamaterials and demonstrate two distinctive examples. First, we use this method to obtain the exceptional points (EPs) of the PT/APT system and observe the spontaneous phase transition of the scattering matrix in the transformation parameter space. Second, by selecting the Jacobian matrix's constitutive parameters, the PT/APT -symmetric system can also be configured to approach the zero and pole of the scattering matrix, behaving as an acoustic coherent perfect absorber and equivalent laser. We envision our proposed CCTA-based paradigm to open the way for exploring the non-Hermitian physics and finding application in the design of acoustic functional devices such as absorbers and amplifiers whose material parameters are hard to realize by using the conventional transformation method.